Neutral Higgs sector of the next-to-minimal supersymmetric standard model with explicit CP violation

The neutral Higgs sector of the next-to-minimal supersymmetric standard model (NMSSM) with explicit $\mathrm{CP}$ violation is investigated at the 1-loop level, using the effective potential method; not only the loops involving the third generation of quarks and scalar quarks, but also the loops involving the W boson, charged Higgs boson, and chargino are taken into account. It is found that for some parameter values of the NMSSM the contributions from the W boson, charged Higgs boson, and chargino loops may modify the masses of the neutral Higgs bosons and the mixings among them significantly, depending on the $\mathrm{CP}$ phase. In ${e}^{+}{e}^{\ensuremath{-}}$ collisions, the prospects for discovering neutral Higgs bosons are investigated within the context of the NMSSM with explicit $\mathrm{CP}$ violation when the dominant component of the lightest neutral Higgs boson is the Higgs singlet field of the NMSSM.